Question

If $x+y\le 2,x\ge 0,y\ge 0$ the point at which maximum value of $3x+2y$ attained will be

• A. $(0,0)$
• B. $(\frac{1}{2},\frac{1}{2})$
• C. $(0,2)$
• D. $(2,0)$

Answer 1

Answer: (D)

Given, $x+y\le 2,x\ge 0$ and $y\ge 0$
Let $z=3x+2y$
Now, table for $x+y=2$

x	0	2	1
y	2	0	1

At $(0,0),0+0\le 2$
$\Rightarrow 0\le 2$, which is true.
So, shaded portion is towards the origin.

$\therefore$ The corner points on shaded region are $O(0,0),A(2,0)$ and $B(0,2)$
At point $O(0,0),z=3(0)+2(0)=0$
At point $A(2,0),z=3(2)+2(0)=6$
At point $B(0,2),z=3(0)+2(2)=4$
Hence, maximum value of $z$ is 6 at point $(2,0)$.